I am mixed up about thermal equilibrium in statistical physics. And I hope you excuse me if I use unconventional words, I am from Sweden, my book is in german and I try to express myself in english. In my book (Noltings "Grundkurs theoretische Physik, Band 6") thermal equilibrium is defined as the state which is characterized by the maximum number of possible realizations. Further, he says that in a system concisting of two subsystems (that can exchange energy) this is exactly when omega_1 * omega_2 has a maximum, where the omegas are the phase space volumes. He goes on to show that this means that the temperature in the two systems is equal. So far so good, and the main argument, that the phase space volume should be maximized, seems plausible, but I can't fully understand it. Could someone give me a hint? Or is this reasoning OK while it leads to results we know are right from experience? I find the book really nice, but this arguing isn't really developed by the author, or is it just way to obvious?